Stripe order in the underdoped region of the two-dimensional Hubbard model

By B. Zheng, Chia-Min Chung, Philippe Corboz, G. Ehlers, M. Qin, R. Noack, Hao Shi, S. White, Shiwei Zhang, Garnet Kin-Lic Chan. Science, 2016

602 citations recorded by the source corpus.

Numerics converging on stripes The Hubbard model (HM) describes the behavior of interacting particles on a lattice where the particles can hop from one lattice site to the next. Although it appears simple, solving the HM when the interactions are repulsive, the particles are fermions, and the temperature is low—all of which applies in the case of correlated electron systems—is computationally challenging. Two groups have tackled this important problem. Huang et al. studied a three-band version of the HM at finite temperature, whereas Zheng et al. used five complementary numerical methods that kept each other in check to discern the ground state of the HM. Both groups found evidence for stripes, or one-dimensional charge and/or spin density modulations. Science, this issue p. 1161, p. 1155 Multiple numerical methods are used to study the ground-state and finite-temperature solutions of the Hubbard model. Competing inhomogeneous orders are a central feature of correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models, even in challenging settings.

Subfields: Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials

View Paper: https://www.semanticscholar.org/paper/ea8786a30f7adfb9d02d04fe666ee6a5fe9330d4

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Citations in the corpus

Stripe order from the perspective of the Hubbard model (2017, background): “The growth of modern computing power combined with recent developments in computational techniques has allowed for significant progress toward understanding static properties of the Hubbard model.(2) However, to connect with experimental results, it has become necessary to determine and benchmark th”
Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods (2017, background): “A recent success is the benchmark study of the Hubbard model [2], and a subsequent multi-method study of the ground-state order in the celebrated 1/8-doped case [3].”
Practical quantum advantage in quantum simulation (2022, background): “Although in one dimension the Hubbard model is exactly solvable 112 , in two dimensions it has been a long-term challenge to find even the lowest-energy states of this model, although a lot of recent progress has been made 40,41 .”
Quantum algorithms to simulate many-body physics of correlated fermions. (2017, background): “state remains ambiguous due to the competition between a number of different order parameters [51].”
Thermodynamics (2021, neutral): “While fermionic and frus-trated spin models in one dimension do not pose any difficulties for MPS-type algorithms in contrast to QMC, they can only be applied to small clusters in dimensions higher than one in which case calculations are usually restricted to the ground state [19, 20].”
Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model (2019, methodology): “At h = 1/8 doping, the ground state has filled stripes with λ = 8 [63].”